Question

Closed form of the recursion formula for $\int_{0}^{1} \ln^r(1-x)x^n \, dx$

score 150 · Answer 1 · 2026-03-25 22:06:08

150

Views

Closed form of the recursion formula for $\int_{0}^{1} \ln^r(1-x)x^n \, dx$

Published on 25 Mar 2026 - 22:06

score 64 · Answer 2 · 2026-03-25 05:34:40

64

Views

Is there a general form of a logical formula with N variables?

Published on 25 Mar 2026 - 5:34

score 132 · Answer 3 · 2023-03-14 10:58:23

132

Views

Does $\lim_{x\to 0} \left(2^{1-x!}3^{1-x!!}4^{1-x!!!}5^{1-x!!!!}6^{1-x!!!!!}\cdot\cdot\cdot\right)^{\frac{1}{x}}=L$ admits a closed form?

Published on 14 Mar 2023 - 10:58

score 103 · Answer 4 · 2026-03-27 18:09:33

103

Views

Continued fraction inequality with well know constant as $\pi$ and golden ratio.

Published on 27 Mar 2026 - 18:09

score 62 · Answer 5 · 2023-03-16 23:16:39

62

Views

The limit of a Nasty Summation

Published on 16 Mar 2023 - 23:16

score 88 · Answer 6 · 2023-03-20 13:36:02

88

Views

Evaluate $\sum_{n=1}^\infty \arctan\frac{1}{n^2}$

Published on 20 Mar 2023 - 13:36

score 173 · Answer 7 · 2026-03-26 09:45:52

173

Views

Simplifying a complicated continued fraction expression.

Published on 26 Mar 2026 - 9:45

score 133 · Answer 8 · 2026-04-01 18:30:04

133

Views

Finding the closed form or tight bound for the number of binary strings with $k$ ones or $k$ zeros and no three consecutive ones

Published on 01 Apr 2026 - 18:30

score 276 · Answer 9 · 2026-03-26 06:31:53

276

Views

Evaluate $\int_{0}^{1} \frac{K(k)E(k)^2-\frac{\pi^3}{8} }{k} \text{d}k$ and $\int_{0}^{1} \frac{E(k)^3-\frac{\pi^3}{8} }{k} \text{d}k$

Published on 26 Mar 2026 - 6:31

score 70 · Answer 10 · 2026-04-01 10:44:39

70

Views

What is the closed form sum of the convolution of non-zero squares?

Published on 01 Apr 2026 - 10:44

score 69 · Answer 11 · 2023-03-26 14:41:30

69

Views

Finding a closed-form of ${\frac{\sum\limits_{n=1}^{x}\frac{1}{\int_{0}^{\infty}e^{-t^{n}}dt}}{x}-1}$ and its improper integral from $1$ to $\infty$.

Published on 26 Mar 2023 - 14:41

score 63 · Answer 12 · 2023-03-28 15:47:18

63

Views

How can I find a closed form for the serie $\sum_{n=0}^\infty (-1)^n \exp(x)^n \exp(y)^{n^2}$?

Published on 28 Mar 2023 - 15:47

score 52 · Answer 13 · 2023-04-02 00:56:31

52

Views

Closed expression for a $\sum\limits_{i=1}^{m} \binom{n+i}{n}$

Published on 02 Apr 2023 - 0:56

score 124 · Answer 14 · 2026-03-26 19:19:01

124

Views

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Published on 26 Mar 2026 - 19:19

score 733 · Answer 15 · 2026-03-30 01:52:02

733

Views

Closed form for the hypergeometic function $\,_{4}F_{3}\left(1,-k,k+\frac{3}{2},\frac{1}{2};\frac{1}{2}-k,k+2,\frac{3}{2};1\right)$

Published on 30 Mar 2026 - 1:52

List Question

Closed form of the recursion formula for $\int_{0}^{1} \ln^r(1-x)x^n \, dx$

Is there a general form of a logical formula with N variables?

Does $\lim_{x\to 0} \left(2^{1-x!}3^{1-x!!}4^{1-x!!!}5^{1-x!!!!}6^{1-x!!!!!}\cdot\cdot\cdot\right)^{\frac{1}{x}}=L$ admits a closed form?

Continued fraction inequality with well know constant as $\pi$ and golden ratio.

The limit of a Nasty Summation

Evaluate $\sum_{n=1}^\infty \arctan\frac{1}{n^2}$

Simplifying a complicated continued fraction expression.

Finding the closed form or tight bound for the number of binary strings with $k$ ones or $k$ zeros and no three consecutive ones

Evaluate $\int_{0}^{1} \frac{K(k)E(k)^2-\frac{\pi^3}{8} }{k} \text{d}k$ and $\int_{0}^{1} \frac{E(k)^3-\frac{\pi^3}{8} }{k} \text{d}k$

What is the closed form sum of the convolution of non-zero squares?

Finding a closed-form of ${\frac{\sum\limits_{n=1}^{x}\frac{1}{\int_{0}^{\infty}e^{-t^{n}}dt}}{x}-1}$ and its improper integral from $1$ to $\infty$.

How can I find a closed form for the serie $\sum_{n=0}^\infty (-1)^n \exp(x)^n \exp(y)^{n^2}$?

Closed expression for a $\sum\limits_{i=1}^{m} \binom{n+i}{n}$

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Closed form for the hypergeometic function $\,_{4}F_{3}\left(1,-k,k+\frac{3}{2},\frac{1}{2};\frac{1}{2}-k,k+2,\frac{3}{2};1\right)$

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